In wireless MIMO communication systems, the use of multiple antennas is much preferred in order to increase the performance of the systems. When multiple antennas at the base station and mobile station are used, the space dimension may additionally be exploited for scheduling the transmission to different users in the systems.
It is well known that in the multi-user MIMO system, there exists parallel channels characterized by mutually orthogonal spatial signature vectors (SSVs) for each user, data pre-coded by these spatial signature vectors can be transmitted simultaneously without co-channel interference (CCI). If the spatial signature vectors of different users are mutually orthogonal, the data of the simultaneous users can be multiplexed in space domain. To improve the link performance of an MIMO system, knowledge of the MIMO channels should be utilized and pre-coding at the transmitter should be performed. A common well-known pre-coding method is to obtain the pre-coding vectors from the singular value decomposition (SVD) of the MIMO channel matrix. Each singular vector form the MIMO channel matrix, also known as a spatial signature vector, corresponds to a spatial data-stream. In accordance with this approach together with a water filling algorithm to distribute the transmit power among the data streams, the channel capacity for the point-to-point Gaussian channel of a single user is achieved.
An OFDM system allows for scheduling of data to users in the time-frequency domain. By using multiple antennas at the base station and the mobile station, users can be scheduled additionally in the spatial domain. When an OFDM time-frequency resource is reused in the spatial domain, this denotes that multiple data-streams are transmitted. Due to the non-orthogonality between spatial data-streams, the data transmitted in different spatial streams for a particular OFDM time-frequency resource, mutually interferes with each other, creating co-channel interference (CCI). Specifically, when transmitting to several users simultaneously in different spatial data-streams of a time-frequency resource in a MIMO-OFDM system, these different users also experience CCI between the multiple data-streams.
Therefore, in contrast to the time-frequency grid in OFDM, which gives orthogonal channels between different users, the further division of the available channels in the space dimension generates a set of channels that generally are not orthogonal to each other. So, for instance, if a time-frequency resource in an OFDM system is allocated to two users at the same time, the transmission to these users mutually interferes with each other due to the co-channel interference.
With the multi-user MIMO-OFDM system, the task of the scheduler is to assign OFDM time-frequency resources, as well as spatial resources to the served users in the coverage of the cell. This task can be overwhelming. The problem is that the optimal resource allocation problem in power, space, time and frequency dimensions has to be done jointly among all the users in the coverage of the cell, due to the non-orthogonality of the spatial dimension that couples the signal to interference ratio of the different users through the co-channel interference. If the MIMO channels hypothetically were orthogonal also in the spatial domain, the scheduler's task would be greatly simplified because it could treat the space, time and frequency domains as orthogonal resources to be allocated to the users.
The non-orthogonality in the spatial domain leads to an extremely complex optimization problem. For example, the paper entitled “MIMO for Long Term Evolution,” which was presented in document R1-050889, 3GPP TSG RAN WG1 Meeting #42, London, UK, 29 Aug.-2 Sep. 2005, relates to a method for resource allocation. Based on unitary matrix pre-coding, data streams from different users are multiplexed in space and time domains. A set of unitary pre-coding matrices is defined off-line. Major steps in the above article are:
1. Each user feedbacks a preferred unitary pre-coding matrix whose column vectors are orthogonal spatial signature vectors. In addition, Channel Quality Information (CQI) for all the pre-coding vectors in the matrix is fed back to the base station;
2. The base station groups users who declare the same preferred unitary pre-coding matrix;
3. The base station selects a group according to a scheduling rule;
4. The base station allocates the orthogonal corresponding pre-coding vectors to users in this selected group according to a scheduling rule;
5. The base station pre-codes different users' data streams by the assigned pre-coding vectors and transmits the pre-coded data streams at the same frequency and time resource.
There are some drawbacks in this scheme:
1) The users are always asked to feedback all available spatial signature vectors and corresponding CQI information. In practice, usually only a few or one of the spatial signature vectors and a few or one of CQI information is necessary in the base station.
2) In this scheme, because users are first grouped according to the same pre-coding matrix, this means that only a subset of the users which select the same pre-coding matrix are possible to be multiplexed in space domain. Although this method can guarantee spatial signature vectors of multiplexed users to be strictly orthogonal, leading to low CCI, in practice, the group of users who can be spatially multiplexed are restricted. Because the probability that more than one user prefers the same pre-coding matrix, which also is a requirement for spatial multiplexing, may be low in some environment especially when the number of users in the cell coverage area is small, which brings out a serious limitation.
3) There exists such a case that users which prefer different pre-coding matrices and have mutually orthogonal space signature vectors can be multiplexed in space with low CCI, however in this scheme the space domain multi-user multiplexing opportunity is lost.
4) The scheme assumes that the selected pre-coding vectors are orthogonal. However, it is easily shown as follows, that this does not assure that the received signals are CCI free.
Assume two users with MIMO channel matrices H1 and H2 respectively. The data x1 to user 1 with the pre-coding vector w1 and the data x2 to user 2 with the pre-coding vector w2 are transmitted. The received signals for user 1 and 2 can then be expressed asy1=H1(w1x1+w2x2)+n1 y2=H2(w1x1+w2x2)+n2 
where n1 and n2 are the respective noise vectors for the two users. The CCI for user 1 is given by the term H1w2x2. In the scheme described above, it is assumed that pre-coding vectors are orthogonal, hence w1*w2=0 is held. To remove the CCI for user 1 completely, it is necessary that w1 is a singular vector to H1 and to remove the CCI for user 2 completely, it is necessary that w2 is a singular vector to H1. Simultaneously w1*w2=0 shall be hold. Hence, complete removal of CCI between two users is very unlikely because it requires a very special relation between the singular vectors of their MIMO channels H1 and H2.
Therefore, there is a problem in the above scheme in that it is premised on the requirement of orthogonal pre-coding vectors wi*wj=0, i≠j, and such a condition that in reality has low significance because CCI in all practical MIMO channels is non-zero anyway.
To increase the opportunities of multiplexing users, especially when there are a low number of MIMO users in the cell coverage area, to obtain an increase in the multi-user diversity gain, the CCI between users multiplexed in space to be larger than zero is allowed. In other words, if the CCI between users multiplexed in space dimension is allowed to be larger than zero, the opportunity of multiplexing users increases and more diversity gain may be obtained in space domain. Thus both more diversity gain obtained in space domain and low CCI exists conflict and the scheme has no ability to solve the conflict between CCI and multi-users diversity gain or to compromise it.
Another scheme is exemplified by an article entitled “An Efficient Resource-Allocation Scheme for Spatial Multi-user Access in MIMO/OFDM Systems,” which is published in IEEE Transactions on Communications, Vol. 53, No. 1, 1, 2005. This article discloses that radio resources are exploited in frequency, time and space domains. Users are grouped according to user's mutual correlations which respectively depend on the maximal SSV selected from spatial signature vectors of each user. The scheduler is to assign the radio resources with the same frequency and time to different users if correlations between any pair of users from different groups are sufficient low, i.e. the users are orthogonal in space domain.
However, the resources allocation scheme is suitable for uplink and only the space mode with maximum gain is considered for each user. In practical wireless communication environments, the grouping criterion may not always be fulfilled. Furthermore, the amount of required feedback signaling is large.